MONTPELIER — Unforeseen budget increases left elected officials wondering Thursday how the state and possibly the city can fund a massive heating project to serve both.

A budget increase on the state’s side of the project led the City Council to go into executive session Thursday night after hearing why the project is $2.3 million over budget, bringing the state’s side to $18.1 million. The state is asking the city to pay $563,948 of the increase.

The state is installing a new heat plant, while the city is extending distribution pipelines to downtown buildings and Union Elementary School.

The budget increases are due in part to an Oct. 1 deadline to have the heating system in place.

“We’re running out of time. It’s getting very tight,” Joe Aja, a project manager for the state, told the council.

Officials said the increases arise from several issues, such as a nearly 2-foot-deep concrete slab floor that must be removed, soil difficulties from rocks and coal ash that will require crews to dig 5 feet deeper than first thought, and limited access and height restrictions for construction staging areas.

City Council member Tom Golonka repeated that the city faces millions of dollars in liability if the project falls apart.

City Manager William Fraser said if the city walked away from the project, there would be at least $2.6 million in charges, such as covering penalties for breaking proposed work schedules. That’s in addition to $2.1 million the city already spent, he said.

Both parties repeated they are committed to the project.

“I’m worried if the Legislature doesn’t give you the $2 million. What happens?” Golonka asked.

“At that time we would have to downsize the project,” said state Buildings and General Services Commissioner Michael Obuchowski.

The deputy commissioner, Wanda Minoli, suggested the project would still need to meet minimum capacity as agreed upon.

Obuchowski said he could see the city paying 24 percent of the additional cost based on contract language. City officials, however, said that cost-sharing was removed from the contract out of financial concerns and through negotiation.

“Now you’re asking us to go back to language that we negotiated out in good faith,” Golonka said. “I’m concerned we’re moving back here.”

Fraser said that if the state was going to design, construct and own the heat plant, the city did not want to be at risk of budget increases for that side of the project.

The council went into executive session around 7:15 p.m. Thursday to discuss strategy.

“We’re in a very difficult position,”Mayor John Hollar said afterward, but he added that the cost for both parties to cancel the project is prohibitively high.

The city does not intend to use money from its general fund, Hollar said, and a narrow operating margin complicates the city’s end of the project, which involves a pipeline for the heat. He said the city’s $4 million portion of the project has only a $200,000 contingency.